This paper studies a wireless sensor system, where packeted information is transmitted to a receiver over a fading channel. The sensor's transmission energy can be chosen within a given interval. To obtain the current channel gain information, the sensor may listen to a pilot signal from the receiver and estimate the channel, which requires energy. When the sensor does not listen to the pilot signal, the transmission energy has to be estimated solely based on other information like the channel gain distribution and past channel information. The sensor is equipped with an energy harvester and a rechargeable battery to temporarily store the harvested energy. The paper derives the optimal energy allocation policy, shows structural properties of the optimal solution and derives a heuristic suboptimal energy allocation policy. The performance of the optimal policy is compared with several other simple policies through numerical examples.